いたす has multiple roles. The three main ones in the context of 敬語 are:
① 謙譲語Ⅰ - talk humbly about one’s own action that affects the target of respect.
This is the form with お or ご that the grammar point mostly talks about. It also includes those する verbs with 拝 etc. But this form can only be used when the person being shown respect is directly affected by a humble action.
Example:
ご説明いたします “I will humbly explain (to you, my superior)”.
② 謙譲語Ⅱ a.k.a. 丁重語 - talk humbly about one’s own action that doesn’t directly affect the target of respect.
This covers cases where a humble action simply affects someone other than the person being shown respect, for example:
田中に説明いたします “I will humbly (with respect to the listener) explain (to Mr or Mrs Tanaka, who is not my superior)”.
It also covers cases where a humble action doesn’t directly affect anyone else at all but the speaker still wants to be humble vs. the listener:
わたくしは朝7時に出発いたします “I will humbly (with respect to the listener) depart at 7 am (but the act of departure does not affect anyone in particular)”.
③ Also usually grouped under 謙譲語Ⅱ a.k.a. 丁重語, but basically used like 丁寧語 - just being “more polite”.
For this use, it’s not even necessary to talk about one’s own action, e.g.:
いい香りがいたします “It smells nice”.
So the questions we have to ask to find out which forms can be used are:
- Is it my own action (or an action of my side)?
- Does it involve the party I’m showing respect to?
In the case of the train departing, this is unfortunately not so obvious.
We could say that while the train departing is not the speaker’s own action, it’s still an action of their side if the speaker represents the company or even group of companies that are involved in operating the train or delivering the service to the customer as a whole.
We could also say that the train’s departure at least affects people on the train.
In the end, the answer to why there is no ご here is that while Japanese people might agree with the first answer, they usually will not agree with the second one. 出発 is something the train does by itself. It’s not an action taken with respect to a specific person or group. Therefore, 謙譲語Ⅰ can’t be used.